Simplify (tan(pi/3))/2+1/(csc(pi/3))

Problem

tan(π/3)/2+1/csc(π/3)

Solution

1. Evaluate the trigonometric functions at the given angle π/3

tan(π/3)=√(,3)

csc(π/3)=1/sin(π/3)=1/√(,3)/2=2/√(,3)

2. Substitute these values back into the original expression.

√(,3)/2+1/2/√(,3)

3. Simplify the second term by taking the reciprocal of the denominator.

1/2/√(,3)=√(,3)/2

4. Combine the two terms since they have a common denominator.

√(,3)/2+√(,3)/2=(2√(,3))/2

5. Reduce the fraction by canceling the common factor of 2

(2√(,3))/2=√(,3)

Final Answer

tan(π/3)/2+1/csc(π/3)=√(,3)

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